6^8 . 2^4 - 4^5 . 18^4/ 27^3 . 8^4 - 3^9 . 2^13

`color{skyblue}{#}``color{red}{m}``color{purple}{a}``color{yellow}{n}``color{pink}{h}``color{brown}{v}``color{magenta}{p}` `color{gold}{2}``color{aqua}{k}``color{orange}{8}`

$$\dfrac{6^8 . 2^4 - 4^5 . 18^4}{27^3 . 8^4 - 3^9 . 2^{13} }$$

$$=\dfrac{(2.3)^8 . 2^4 - (2^2)^5 . (3^2.2)^4}{(3^3)^3 . (2^3)^4 - 3^9 . 2^{13} }$$ $$=\dfrac{2^8.3^8.2^4-2^{10}.3^8.2^4}{3^9.2^{12} - 3^9 . 2^{13}}$$

$$=\dfrac{2^{12}.3^8-2^{12}.3^8.2^2}{3^9.2^{12} - 3^9 . 2^{12}.2}$$

$$=\dfrac{(1-2^2).12^{12}.3^8}{3^9.(1-2).12^{12}}$$

$$=\dfrac{1-4}{(-1).3}$$

$$=\dfrac{-3}{-3}=1$$

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